Dumb question about Photoshop

I'm trying to make a transparent background for a simple graphics image in Photoshop. I select the background using the Magic Wand or Quick Selection, and press Delete. Sometimes this works (background turns to checkered), but sometimes I get a Fill dialog which asks how I want to set up Contents and Blending, and I can't get any further from there. I feel like I'm missing something really basic, but what is it?
Any help appreciated ...

It sounds like you're working with a background layer, which Photoshop treats differently to other layers. Try duplicating the layer, making the original background layer invisible and working with the duplicate.